Question

In a recent survey, 64 % of the community favored building a police substation in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the police substation.

Answer 1

Answer: 0.1840

Step-by-step explanation:

The binomial probability formula :-

$P(X)=^nC_x\ p^x(1-p)^{n-x}$, here n is the number total of trials , p is the probability of getting success in each trial and P(x) is the probability of getting success in x trial.

Given : The probability of the community favored building a police substation in their neighborhood = 0.64

If 14 citizens are chosen, then the probability that exactly 8 of them favor the building of the police substation will be :-

$P(8)={14}^C_{8}\ (0.64)^{8}(1-0.64)^{14-8}\\\\=\dfrac{14!}{8!6!}\times(0.64)^8(0.36)^{6}\\\\0.183996740126\approx0.1840$

Hence, the probability that exactly 8 of them favor the building of the police substation = 0.1840